two kinds of statments a boy can say which can not be said true or false
1- He can ask a question for example : Are you serious? or are you mad or something?
2- He can give an order or requset for example get off my way or He can say : Hey look at me

The boy either says nothing and go,without crossing the bridge, because anywhere it is said that he must cross the bridge. He just came across it. or he can say to the man I do not want to cross the bridge.

” you are going to chop my head off”
Explanation: If the man says this statement is true then he should strangle the boy to death according to what he informed which is against what the statement says! If he says this statement is false that means he is going to contradict himself as well!

Its about the statement being true or false on which the punishment will depend.. if the boy says ‘you are going to chop my head off’ like you said, than its the statement that becomes a true statement and than the axe man can easily punish him and strangle him to death as he has never said that he will follow the statement that the boy will say to him.. hope you understand my point which makes your explanation FALSE. Don’t Mind please.. 🙂

the boy may ask : You will kill me.
if the man thinks the answer is wrong then he will try to kill him, contradicting him,
If the man thinks the answer is wright then he have to allow the boy to cross the bridge, then he can’t kill the boy, again contradicting him